Electric field excited in air by a pulse of gamma rays

The characteristics of the electric field produced by air polarization during the passage of nonstationary Compton currents excited by a -ray pulse in low-density air are discussed. The influence of the field on the motion of the Compton electrons is taken into account. The amplitude and relaxation time of the field are evaluated. A polarization electric field is created through the action of a directed current of -rays in air because of the movement of the Compton electrons. This paper discusses the basic characteristics of the resultant field in low-density air. A similar problem was raised in [1], where the electromagnetic field excited by a nonstationary source of -radiation in the upper atmosphere was considered. In that case, the Compton-electron currents were specified and their magnitude was assumed to be proportional to the ratio between the gas kinetic ranges of Compton electron and -ray (this ratio is of the order of 0.01 and is indepenent of height). With an increase in electron range, however, the decelerating action of the resultant electric field on the motion of the Compton electron becomes important (eE/ is a criterion for the effect; E is the field intensity, and and are the range and energy of the Compton electron).Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 3–8, July–August, 1970.In conclusion, the authors thank G. M. Gandel'man for several discussion.     

Asymptotic solution to the problem of hypersonic flow over bodies in the neighborhood of the separation point of a thin shock layer

A study is made of the problem of hypersonic flow of an inviscid perfect gas over a convex body with continuously varying curvature. The solution is sought in the framework of the asymptotic theory of a strongly compressed gas [1–4] in the limit M when the specific heat ratio tends to 1. Under these assumptions, the disturbed flow is situated in a thin shock layer between the body and the shock wave. At the point where the pressure found by the Newton-Buseman formula vanishes there is separation of the flow and formation of a free layer next to the shock wave [1–4]. The singularity of the asymptotic expansions with respect to the parameter ₁ = ( –1)/( + 1) associated with separation of the strongly compressed layer has been investigated previously by various methods [3–9]. Local solutions to the problem valid in the neighborhood of the singularity have been obtained for some simple bodies [3–7]. Other solutions [7, 9] eliminate the singularity but do not give the transition solution entirely. In the present paper, an asymptotic solution describing the transition from the attached to the free layer is constructed for a fairly large class of flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 99–105, January–February, 1982.     

Self-consistent problem about electric fields produced in air by a pulse of gamma quanta

The problem of the radial electric field excited in air by an instantaneous point source of gamma quanta is considered. This problem was solved in [1–3] under the assumption that the Compton electron currents originating during scattering of the gamma quanta are given. Such an approximation is valid if the influence of the originating electric field on the Compton electron motion is neglected. The dimensionless parameter characterizing the influence of the electric field is α = e?1/W (? is the characteristic magnitude of the electric field, and 1 and W are the path and kinetic energy of the Compton electron, W ～ 1 MeV). For α ? 1 deceleration of the electrons by the electric field can be neglected and the model proposed for Compton currents [1] is used to determine the field.     

Calculation of the motion of relativistic beams of charged particles in electromagnetic fields

In calculating high-current relativistic beams of charged particles moving in electromagnetic fields, it is necessary to take account of the effect of the electric and magnetic self-fields products by the beams themselves. This effect has been modeled on a computer [1, 2]. The present paper describes numerical algorithms contained in the KSI-BÉSM compiling system [3] which permit the inclusion of a broad class of relativistic problems, taking account of the magnetic field of currents flowing in the metal parts of the device being calculated, and also problems with virtual cathodes.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 3–8, May–June, 1979.     

Distribution of radiant thermal flux over the surface of a sphere for hypersonic flow of a nonviscous radiating gas past the sphere

In the present study using the Newtonian approximation [1] we obtain an analytical solution to the problem of flow of a steady, uniform, hypersonic, nonviscous, radiating gas past a sphere. The three-dimensional radiative-loss approximation is used. A distribution is found for the gasdynamic parameters in the shock layer, the withdrawal of the shock wave and the radiant thermal flux to the surface of the sphere. The Newtonian approximation was used earlier in [2, 3] to analyze a gas flow with radiation near the critical line. In [2] the radiation field was considered in the differential approximation, with the optical absorption coefficient being assumed constant. In [3] the integrodifferential energy equation with account of radiation was solved numerically for a gray gas. In [4–7] the problem of the flow of a nonviscous, nonheat-conducting gas behind a shock wave with account of radiation was solved numerically. To calculate the radiation field in [4, 7] the three-dimensional radiative-loss approximation was used; in [5, 6] the self-absorption of the gas was taken into account. A comparison of the equations obtained in the present study for radiant flow from radiating air to a sphere with the numerical calculations [4–7] shows them to have satisfactory accuracy.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 44–49, November–December, 1972.In conclusion the author thanks G. A. Tirskii and É. A. Gershbein for discussion and valuable remarks.     

Derivation of the equations of slow nonisothermal gas flows

In recent years, some new phenomena have been predicted theoretically on the basis of the Burnett approximation. These include thermal-stress and concentration-stress convection [1–3], and also effects due to the influence of a magnetic field in a multiatomic gas (viscomagnetic heat flux, etc., [4]). It has been shown theoretically (see [5]) that under certain conditions various terms of the Burnett approximation must be taken into account in the expression for barodiffusion. The conclusions relating to a viscomagnetic heat flux have recently been confirmed experimentally [4]. The predicted phenomena follow rigorously from the Burnett equations. However, many hydrodynamicists adopt a sceptical attitude to these equations, which is due partly perhaps to attachment to the classical Navier-Stokes equations, which have served theoreticians without fail for a century and a half. In this connection, we discuss the evolution of ideas relating to the validity of the Burnett approximation. We discuss the minimal assumptions which must be made in order to derive the equations of slow [Reynolds number R = 0(1)], essentially nonisothermal [ ln T = 0(1)] flows of a gas as a continuous medium (Knudsen number K O) in the case when the derivatives of the thermal Burnett stresses in the momentum equation have the same order of magnitude as the Euler and Navier-Stokes terms of this equation [1–3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 77–84, November–December, 1979.We thank G. I. Petrov and L. I. Sedov for discussions that stimulated the above analysis.     

Nonlinear fluctuations in a plasma with Coulomb interaction

The theory of thermodynamic plasma fluctuations is now fairly well developed [1–31]. However, in practice, one often comes across plasma states which are very far from being in equilibrium. Flucuations in such nonequilibrium states have been investigated by a series of authors [4–9] in terms of a linear approximation.It must, however, be noted that, under specific conditions, neglect of nonlinear effects may turn out to be unjustified. This relates particularly to plasma states which are close to being unstable. In this region the fluctuations of various physical quantities are very large. A similar situation occurs, for example, in the experimentally observed critical opalescence in plasma, i.e., the anomalously strong scattering of electromagnetic waves by an unstable plasma [10]. The dependence of the transport coefficient on ion-sound oscillations at a fairly large ratio of electron and ion temperatures [11] is another example illustrating the insufficiency of the linear approximation. Finally, nonlinear effects may be significant in a plasma with highly developed turbulence.All this points to the necessity of expressing the various correlation functions characteristic of fluctuation processes in terms of higher correlation functions. In doing so, it is natural to confine oneself, for a start, to the first approximation in order of nonlinearity.The present paper solves this problem for plasma with Coulomb interaction.     

Electroconvective stability of a weakly conducting liquid

In inhomogeneous electric fields, at sufficiently high field strengths, a weakly conducting liquid becomes unstable and is set in motion [1–4]. The cause of the loss of stability and the motion is the Coulomb force acting on the space charge formed by virtue of the inhomogeneity of the electrical conductivity of the liquid [4–13]. This inhomogeneity may be due to external heating [4–6], a local raising of the temperature by Joule heating [2, 7, 8], and nonlinearity of Ohm's law [9–13]. In the present paper, in the absence of a temperature gradient produced by an external source, a condition is found whose fulfillment ensures that the influence of Joule heating on the stability can be ignored. Under the assumption that this condition is satisfied, a criterion for stability of a weakly conducting liquid between spherical electrodes is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–142, July–August, 1979.     

Flow of a conductive gas in a circular tube in a strong axiosymmetric magnetic field

The flow of a conductive gas along a channel in an external axiosymmetric magnetic field with a finite value of the magnetogasodynamic parameter N is examined. Numerical flow calculations are performed for a circular tube in such a field. Gas dynamic parameter fields, total pressure losses, and electric current intensities with the presence of transsonic zones and highly compressed regions are determined. Through comparison of the results obtained with linear theory data, the range of applicability of the latter is determined. Of the works dedicated to study of flow in external magnetic fields with N1, we should take note of [1], in which the process of entry of the gas into a transverse magnetic field was examined; [2], which studied one-dimensional transient motion with shock waves; and [3], where mixed flow in a Laval nozzle with an axiosymmetric homogeneous magnetic field was studied. Flow in a circular tube was examined in [4]; but the analysis performed by the characteristic method permitted calculation of only the initial supersonic flow zone. Motion in circular tubes in the presence of an axiosymmetric, magnetic field was studied in the linear formulation in [4, 5].Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 145–155, September–October, 1972.     

Nonmonodisperse breakup of capillary jets in a variable electric field

The electrical charging of capillary jets has a strong influence on their stability [1–10]. Well-known theoretical studies have been devoted to the linear [1–6], weakly linear [7], or finite-amplitude [10] stability of such jets in a constant electric field. In the present paper, an investigation is made in the framework of the full nonlinear equations. The main attention is devoted to effects associated with allowance for a time-variable electric field. It is shown that a sharp decrease of the surface charge may lead to an appreciable decrease in the size of the satellite droplets; allowance for the long-wavelength background also leads to a decrease in the size of the satellite droplets. In contrast, a sharp increase of the surface charge increases the relative contribution of the satellite droplets. At the same time, introduction of small-scale background perturbations can lead to a decrease in the contribution of the fine satellite droplets and to a weakening of their reaction to a rapidly increasing electric field. It is shown that the degree of monodisperseness can be increased by a relatively slowly varying electric field. An averaged effect of an electric field that varies rapidly in time is found. Appreciable increase of the initial perturbation amplitude in the case of a periodically varying electric field can lead to an appreciable increase in the degree of monodisperseness. The introduction of short-wavelength perturbations in a periodic electric field with large amplitude of the pulsations can lead to disappearance of the satellite droplets.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 55–62, March–April, 1991.     

Nonlinear stabilization of unstable acoustical vibrations in a bounded heat-evolving medium

The working process in many power units, taking place with the evolution of energy, under determined conditions is acoustically unstable in a linear approximation. The problem of determination of the amplitudes of the unstable waves, set up as a result of the pumping of energy from the unstable mode to the damping mode with their linear interaction is of practical interest. In this paper equations are derived for the fully established amplitudes of plane acoustical vibrations in a three-wave approximation, taking account of boundary impedances, breaking down the internal resonance of the acoustical overtones excited. The discussion regards a high-temperature heat-evolving gas, whose general stability conditions were formulated in [1] and discussed also in [2, 3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 34–41, November–December, 1978.     

Theory of the supersonic part of a nondissipative box-type accelerator

This paper calculates the two-dimensional flow of a two-component cold nondissipative plasma. The condition is found for which a nondissipative plasma can escape from a magnetic field.A distinction must be made between those plasma accelerators which operate at high densities n10¹⁶cm^–3 and those which operate at low densities (n10¹⁴ cm^–3).In the first case the acceleration of ions may occur not only as a result of internal electric fields, but also as a result of the collision of ions with each other (ordinary thermal acceleration) or the collision of ions with elections moving as a result of the Hall^* effect along the accelerator channel.In the second case the only mechanism capable of accelerating the ions is the internal longitudinal electric field [1, 2]. This treatment excludes those systems [3], in which the ions are accelerated as a result of kinetic instabilities.The present paper treats the acceleration of a low-density plasma. A box-type accelerator has been chosen by way of example, since in this case the peculiarities of low-density accelerating systems are particularly marked.Three conditions must be fulfilled in order to create a box-type accelerator operating at low densities.Firstly, we must make use of segmented electrodes, since otherwise it is impossible to create in the space inside the accelerator electric fields of the type (2.11) necessary for accelerating the plasma. For continuous electrodes the structure of the electric field in the space inside the accelerator results from the superposition and interaction of exceedingly complex processes at the boundaries and in the vicinity of the electrodes.Secondly, if the system under consideration is intended to produce high velocities, then it is necessary to create conditions under which there is no interaction of the fast particle flux with the walls. In other words, the current in the system must be controlled electromagnetically and not by means of the walls, which is the case in ordinary gasdynamic nozzles.It should be noted that in high-velocity plasma accelerators which produce ions with energies 100, it is essential to eliminate the interaction of the current with the walls at higher densities also. Thirdly and lastly, conditions must be created which ensure the escape of the plasma from the magnetic field.It was shown in [4] that the magnetic field is in factfrozen into the electronic component of the plasma, and so a necessary condition for a compensating current to escape from the magnetic field is that the exchange parameter §1 should be large.The present paper develops the theory of the supersonic part of a box-type accelerator. It should be noted that many papers [5–8] have been devoted to the theory of the box-type accelerator. These, however, were written on the assumption either that the medium is incompressible or for the quasi-one-dimensional approximation in which the flow is of necessity given a particular geometry. These assumptions are, of course, very far removed from reality, at least as far as the production of high-velocity flows is concerned.In conclusion the author is grateful to A. I. Bugrov, L. E. Kalikhman, and L. S. Solov'ev for discussing the questions raised.     

Propagation of planar shock waves in an exponential atmosphere

We consider planar explosions in a medium with an exponential density distribution. In contrast to the so-called sectorial approximation [1] we take into account the overflow of energy from a lower region to an upper region, so that our solution of the problem considered here gives a truer picture of the flow of the gas at a later stage of a point explosion in a nonhomogeneous atmosphere. The numerical solution in both upper and lower regions of the flow merges into the corresponding limiting self-similar regime [2, 3]. The calculations are carried out up to a gap in the atmosphere [4]. The computational method is based on implicit difference approximations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 5, pp. 31–35, September–October, 1971.The authors are deeply grateful to L. A. Chudov for his constant interest in our work and for useful discussions, and they also wish to thank É. I. Andriankin for meaningful discussions of the paper.     

Calculation of inviscid radiating gas flow past a blunt body

During hypersonic gas flow past a blunt body with a velocity on the order of the escape velocity or more, the gas radiation in the disturbed region behind the shock wave becomes the primary mechanism for aerodynamic heating and has a significant effect on the distribution of the gasdynamic parameters in the shock layer. This problem has been considered from different points of view by many authors. A rather complete review of these studies is presented in [1–4].In earlier studies [5, 6] the approximation of bulk emission was used. In this approximation, in order to account for the effect of radiative heat transfer a term is added in the energy equation which is equivalent to the body efflux, whose magnitude depends on the local thermodynamic state of the gas. However, the use of this assumption to solve the problem of inviscid flow past a blunt body leads to a singularity at the body [7, 8]. To eliminate the singularity, account is taken of the radiation absorption in a narrow wall layer [7], or the concept of a viscous and heat-conductive shock layer is used [8]. A further refinement was obtained by Rumynskii, who considered radiation selectivity and studied the flow of a radiating and absorbing gas in the vicinity of the forward stagnation point of a blunt body.In the present paper we study the distribution of the gasdynamic parameters in the shock layer over the entire frontal surface of a blunt body in a hypersonic flow of a radiating and absorbing gas with account for radiation selectivity.     

Flow of a viscous fluid in a closed cavity in the presence of slip effects

Slip at the wall is observed in the flow of non-Newtonian fluids [1–4] and rarefied gases [5]. The most complete information on the phenomenon is obtained in capillary viscosimetry. For small radii of the capillaries and in porous media the slip effect is manifested even for Newtonian fluids (water, kerosene, for example) [6]. Experiments [2, 4] show that the influence of the entrance section can be ignored if the length of the capillary exceeds its radius by about 100 times. For the measurement of the rheological characteristics of high-viscosity fluids the use of long capillaries is difficult, and it is necessary to calculate the two-dimensional flow at the entrance section with allowance for slip. The need for such calculations also arises, for example, when one is choosing the optimal parameters of the screw devices employed in the processing of polymers [7]. Two-dimensional flows of a viscous incompressible fluid are frequently calculated with the flow function and vorticity =– used as variables [8–14]. The expressions for the vorticity on the boundary are usually obtained from the viscous no-slip condition [8, 9]. In the present paper, expressions are obtained for the vorticity on a wall in the presence of slip. The obtained expressions are used to solve a test problem on the flow of a viscous incompressible fluid in a cavity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 10–16, January–February, 1980.     

Internal rotation in the hydrodynamics of weakly conducting dielectric suspensions

Hydrodynamic phenomena in weakly conducting single-phase media due to interphase electric stresses are reviewed in [1]. In the present paper, a model is constructed of a dielectric suspension with body couples due to the field acting on free charges distributed on the surface of the particles of the suspension. Averaging of the microscopic fields yields macroscopic equations for the field and the polarization of the dielectric suspension with allowance for the finite relaxation time of the distribution of the free charge on the phase interface. The developed model is used to consider the occurrence of spontaneous rotation of a dielectric cylinder in a weakly conducting suspension in the presence of an electric field; compared with the case of single-phase media [2], this is characterized by a significant reduction in the threshold intensity of the electric field with increasing concentration of the particles [3]. In the present model of a dielectric suspension, the destabilization of the cylinder is due to the occurrence of rotations of the particles of the suspension due to the interaction between the polarization and the motion of the medium. The relaxation equation for the polarization for the given model is analogous to the corresponding equation for media which can be magnetized [4–6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 86–93, March–April, 1980.     

Steady flow around a plane cascade by an ideal gas

The steady separation-free flow around a flat cascade by an ideal gas is discussed. Most of the attention is devoted to blocking regimes with a supersonic velocity in the entire flow and its subsonic component normal to the front of the cascade. A directing action of the cascade (the direction of the velocity and the Mach number of the advancing flow turn out to be related) is exhibited in these regimes which is a consequence of an independence of the flow in front of the cascade of the conditions behind it [1–5]. The most widespread method of their calculation [3, 4, 6] is based on the method of characteristics with establishment of the flow outside the cascade in a timelike coordinate. Although the integrated conservation laws also permit finding the parameters at infinity, the numerical construction of as long-range fields as desired with periodic sequences of attenuating discontinuities is practically impossible. The approximation of nonlinear acoustics (ANA) [7, 8] is justified here, as it is very effective in such problems [8–12]. A combination of ANA, the integrated conservation laws, and establishment in a calculation according to [13, 14] with isolation of the discontinuities has been realized in [5] for the construction of a solution on the entrance section of a cascade and everywhere in front of it. Below the method of [5] is extended to the entire flow and simplified even more. The flow on the entrance section of the cascade is, just as in [3], found in the approximation of a simple wave, in the rest of it and in a finite strip behind it-the flow is found with the help of the straight-through version of the scheme of [13, 14], and in the long-range field-in the ANA. A simpler version is proposed. In it ANA is applied outside the cascade and the linear theory is applied inside the cascade. Examples of the calculations are given. Similarity laws are formulated for all the regimes of streamline flow.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 35–43, November–December, 1984.     

Investigation of supersonic flow around a blunt body with injection for high Reynolds numbers

The paper discusses the supersonic flow around a blunt smooth body by a stream of viscous gas with subsonic injection from the surface of the body. The effect of various injection cycles on the physical flow characteristics ahead of the body are studied in [1, 2]; the problem is considered in the approximation of a boundary layer. The nonuniform composition of the gas ahead of the body, chemical reactions between the various components, and the effect of radiation are taken into account. For a number of flow cycles, which are of practical importance, it will be of interest to consider higher approximations in powers of [=1/Re, see Eq. (1.1) below] in the shock layer ahead of the body and, in particular, to explain the action of the displacement effect and also the limits of applicability of the boundary-layer approximation assumed in [1, 2]. Extensive literature has been devoted to the asymptotics of the problem of flow around a blunt body of a viscous gas at high Reynolds numbers (see, for example, Van Dyke's book [3]). An investigation of the problem, based on the method of M. I. Vishik and L. A. Lyusternik, is contained in [4–6]. (The advantage of the use of Vishlik and Lyusternik's method in comparison with the method of internal and external expansion is discussed in [4].) The effect of injection on the flow has not been considered in the papers listed. In this paper, approximate solutions are constructed with an error of order and ² which take into account the effect of the injectionf on the flow . The approximate solutions are compiled from a more accurate nonviscous flow (external solution) and boundary-layer corrections. The boundary-layer corrections are constructed on a shock wave and a contact boundary in such a way that the solution would be continuous and quite smooth. For the external solution at the contact boundary, conditions are obtained which take into account the effect of viscosity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 69–77, January–February, 1974.     

Multiscale simulation of viscoelastic free surface flows

A micro–macro approach based on combining the Brownian configuration fields (BCF) method [M.A. Hulsen, A.P.G. van Heel, B.H.A.A. van den Brule, Simulation of viscoelastic flow using Brownian configuration fields, J. Non-Newtonian Fluid Mech. 70 (1997) 79–101] with an Arbitrary Lagrangian–Eulerian (ALE) Galerkin finite element method, using elliptic mesh generation equations coupled with time-dependent conservation equations, is applied to study slot coating flows of polymer solutions. The polymer molecules are represented by dumbbells with both linear and non-linear springs; hydrodynamic interactions between beads are incorporated. Calculations with infinitely extensible (Hookean) and pre-averaged finitely extensible (FENE-P) dumbbell models are performed and compared with equivalent closed-form macroscopic models in a conformation tensor based formulation [M. Pasquali, L.E. Scriven, Free surface flows of polymer solutions with models based on the conformation tensor, J. Non-Newtonian Fluid Mech. 108 (2002) 363–409]. The BCF equation for linear dumbbell models is solved using a fully implicit time integration scheme which is found to be more stable than the explicit Euler scheme used previously to compute complex flows. We find excellent agreement between the results of the BCF based formulation and the macroscopic conformation tensor based formulation. The computations using the BCF approach are stable at much higher Weissenberg numbers, (where λ is the characteristic relaxation time of polymer, and is the characteristic rate of strain) compared to the purely macroscopic conformation tensor based approach, which fail beyond a maximum Wi. A novel computational algorithm is introduced to compute complex flows with non-linear microscopic constitutive models (i.e. non-linear FENE dumbbells and dumbbells with hydrodynamic interactions) for which no closed-form constitutive equations exist. This algorithm is fast and computationally efficient when compared to both an explicit scheme and a fully implicit scheme involving the solution of the non-linear equations with Newton’s method for each configuration field.     

Instability of a hypersonic flow over a wedge in the Newtonian approximation

At the present time, there are a number of works in the literature that treat unsteady hypersonic flows in the Newtonian approximation [1–4]. Since the angle of incidence of the shock wave _s coincides in the zero-order approximation with the angle of inclination of the bodys [1], the latter is usually used in the boundary conditions on the shock. However, in the zero-order approximation _b can be used with the same justification. Both approaches are equally justified and give similar results for a steady flow. For unsteady flows the results can differ radically. It will be shown below that for an investigation of a flow over a fixed wedge with constant conditions in the free stream a steady-state pattern is obtained in the first case and a solution growing in time, in the second case.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 158–160, July–August, 1976.